Abstract: This is the title of my new book, due to be published shortly by Springer. It is a research level monograph of about 700 pages, where much of the material has previously been available only in journal articles. Random measures play a fundamental role in many areas of stochastic processes and their applications, and their theory deserves to be better known. In this talk I will give a general overview, and perhaps highlight some topics of special interest, without going into too much technical detail.